The Dons had failed to find the back of the net in their first four matches of the new SPL campaign but it took them only 12 minutes to take the lead, Rob Milsom slotting home after fine play by Josh Magennis.
The home side doubled their advantage after 27 minutes when Scott Vernon took full advantage of a defensive mistake by Caley debutant Roman Golobart to drive the ball past Ryan Esson.
Inverness pulled a goal back with 11 minutes remaining when Richie Foran seized upon Youl Mawene's careless header to fire past David Gonzalez.
Paul Burns struck a late winner against Dundee United at Tannadice to send Dunfermline into third place with a 1-0 victory.
The former Queen of the South midfielder drove home his first SPL goal from 20 yards as the Pars leapfrogged Rangers in the table.
Two goals in the final three minutes of the first half helped St Mirren to a 2-1 away victory over Hibernian.
Goals from former Cardiff striker Steven Thompson and a clinical strike from his midfield namesake Steven Thomson on the stroke of half-time consigned Hibernian to their second successive league defeat.
Garry O'Connor had put Hibs ahead in the first half.